Question

Much is still to be learned about the relationship between sound frequency and loudness. One way to study this relationship is to have listeners perform loudness judgments for tones of different frequences. For each listener, the output of these judgments is a number, measured in sones, that gives the loudness of the tone relative to the loudness of a reference tone. You have in front of you data from an experimental study in which 54 listeners were asked to perform such loudness judgments for tones of various intensities and frequencies. Of these 54 listeners, 18 had normal hearing, 18 used hearing aids, and 18 had some hearing loss at low frequencies (but didn't use hearing aids). Here is a summary of the data obtained for a 50 dB SPL, 500Hz tone (the data are the sone values corresponding to this tone): Groups Sample Sample Sample variance Normal hearing 2.40 0.17 Hearing aid 0.29 Some hearing loss 0.22 Are there differences in the mean sone values for this tone for the populations of listeners with normal hearing, Isteners with hearing aids, and listeners with low-frequency hearing loss? We can perform a one-way, Independent samples ANOVA test to answer this question, such a test uses the statistic Variation between the samples Variation within the samples size mean 18 18 18 2.20 2.14 For the data summarized above, F 1.47

Answer 1

Ans: 1.47 So Fa variation between the samples Variation within the samples Under Ho..F follows for distribution with degrees of freedom ( K-1, n-k), where k=3, no. of samples and h= 54, total no. of observations- En F (2,51) The p-value is obtained wing fermula wie = pr(F1>1.47)* = 0.2 395 greater Since p-value is than a 20.05, we conclude that there are no differences in the mean some values this. the three groups. That is we do not conclude that there in differences od in the mean sone values among three groups. P-vakie done amung (No for the